1. Physics – Chapter 3-1 Introduction to Vectors
St. Augustine Preparatory School
September 4, 2015

2. Two dimensional motion
Previously in Chapter 2 we talked about objects moving left/right or up/down or ahead/backwards, but we never combined more than one dimension.
Although this is a great place to start, most of the motion in our world that we want to describe is at least two dimensional.

3. Terminology
Scalar Quantity: Quantity that has magnitude (a number) but no direction. Ex. Speed, distance Vector Quantity: Quantity that has both magnitude and direction Resultant: The answer found by adding two vectors

4. Vector Notation
We show that a quantity is a vector by drawing an arrow above its symbol in a formula (example: v)

5. Drawing Vector Diagrams
We use arrows to draw vector diagrams
Arrow length should represent the quantity of an arrow in comparison to the rest
Arrows are drawn “tip to tail”

6. Drawing Vector Diagrams
Example: Mary walks 5 km north before turning and walking 12km east. Draw the vector diagram for Mary’s walk.

7. Drawing Vector Diagrams
Example: Mary walks 5 km north before turning and walking 12km east. Draw the vector diagram for Mary’s walk.
12km
5km

8. Qualities of Vectors
Vectors can be added in any order. Consider the path of a runner below.

9. Finding the resultant vector
The resultant vector is found by adding two vectors.
If the vectors make a 90° triangle, we will use the Pythagorean Theorem (a2 + b2 = c2)
Example: Mary walks 9m north and 6m east. What is Mary’s displacement?

10. Finding the resultant vector
Example: Mary walks 9.0m north and 6.0m east. What is Mary’s displacement?
We want to calculate
the length of the red
vector
6.0m
9.0m

11. Practice Problems
1) Mary walks 13.3 m east and 7.0m north. What is Mary’s displacement? 2) Mary walks 1.32km south and then 4.2km east. What is Mary’s displacement?

12. Direction of the Resultant
Positive and negative is no longer going to be effective in describing direction.
Example:
The orange resultant vector is in a north direction (positive) and a west direction (negative) so would it be positive or negative?

13. Using the tangent (tan) function
Trigonometry:
θ (called theta) is the angle in degrees
(Make sure your calculator is set to degrees)
tan-1 is the inverse function of tan

14. Finding the resultant vector
Example: Mary walks 9.0m north and 6.0m east. What is Mary’s displacement? Find the angle of Mary’s displacement
We want to calculate
the length of the red
vector
6.0m
9.0m θ

15. Practice Problem
Mary walks 7.6km south and 3.9km east. What is the magnitude and angle of Mary’s displacement?